Sustainable Cities and Society 54 (2020) 101997

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Sustainable Cities and Society

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Mapping spatial distribution of particulate matter using Kriging and Inverse T

Distance Weighting at supersites of megacity Delhi
Komal Shuklaa, Prashant Kumarb, Gaurav S. Manna, Mukesh Kharea,c,*
a
Department of Civil Engineering, Indian Institute of Technology, Delhi, New Delhi, India
b
Global Centre for Clean Air Research (GCARE), Department of Civil and Environmental Engineering, Faculty of Engineering and Physical Sciences, University of Surrey,
Guildford, GU2 7XH, United Kingdom
c
Centre of Excellence for Research on Clean Air, Indian Institute of Technology, Delhi, New Delhi, India

A R T I C LE I N FO A B S T R A C T

Keywords: Anthropogenic airborne particulates are among the major contributors to urban air pollution and pose a sig-
Spatial interpolation nificant health risk. Particulate matter has emerged as a serious pollution threat in India, specifically to the
Discrete predictions capital—New Delhi. The objective of this study is to map PM2.5 profile using two widely used spatial inter-
Ordinary kriging (OK) polation techniques (Kriging and IDW) by predicting their concentrations at distinct unmonitored locations. The
Inverse distance weighted (IDW)
implemented methodology has a wide-scoped utility in the field of air pollution; especially in Low-Middle
Prediction accuracy
ASAP-Delhi project
Income Countries where setting up new monitoring stations include financial/logistical/location problems. The
generated maps can help in policy formulation and decision making by providing aid in PM2.5 visualisation of
spatial and temporal variability. First phase of study involves prediction of concentrations at two sites (re-
inforcing the need for sustainable development of the city) using concentrations for 2015–2017. In the second
phase, pollutant mixing ratios were obtained for four winter months between Nov-2017 to Feb-2018 at 17
monitoring stations. In this phase, predictions were made for 11 supersites (zones of important land-use). The
average error of Kriging and IDW (taking both phases) was ∼22 % and 24 %, respectively. The magnitude of
change in the daily concentration was relatively negligible and annual trend can be identified.

1. Introduction efficiently to ensure long lasting quality life for the city and the in-
habitants (Silva, Khan, & Han, 2018).
The impact of air pollution on human health in both developed and Particulate matter (PM) is the net sum of all particles suspended in
developing nations are significant (Chung, Zhang, & Zhong, 2011; the air (Heal, Kumar, & Harrison, 2012). The focus of this work remains
Fotourehchi, 2016; Kanada et al., 2013). Episodes of spikes in air pol- on PM2.5, which is referred to PM that has an aerodynamic diameter of
lution concentrations have increased in frequency over the last decade ≤2.5 μm (Kumar, Patton, Durant, & Frey, 2018). Air pollution from
(Cohen et al., 2017; Shukla, Srivastava, Banerjee, & Aneja, 2017). Each onsite burning of agricultural crop residue is one of the many causes of
year about 800,000 deaths and around 4.6 million lost life-years are environmental hazard observed in northern India (Awasthi et al.,
caused by air pollution (WHO, 2016). It has attracted attention from the 2011). Considerable significance is held by the phenomenon of the
Supreme Court of India (Rosencranz & Jackson, 2003), non-govern- Asian Brown Cloud, and its multifarious impacts. It affects agriculture,
mental organizations (Greenstone & Hanna, 2014) and numerous pol- health and climate change on both regional and global scale (Srinivasan
icymakers (Kandlikar & Ramachandran, 2000). In India, the prime air & Gadgil, 2002). In cities such as Delhi, air pollution is attracting the
pollution monitoring agency is the Central Pollution Control Board attention from the administrators and policy makers, which has opened
(CPCB), which monitors air pollution through 731 nation-wide mon- the way for a higher-level tactical approach to mitigate these problems
itoring stations (CPCB, 2018). Delhi lacks significant natural water (Kumar, Gulia, Harrison, & Khare, 2017). The unavoidable migration
bodies, which intensifies the effect of PM2.5 among other pollutants and towards the urban area gives way to analysing its effect on the natural
contributes to medical complications in various age groups. As per the resources and infrastructural capabilities of the cities (Silva & Mendes,
latest policy of the Delhi government is the epitome of the integrated 2012). Recent studies point out that vehicular particulate emissions
approach to smart cities, and its integrated systems need to function have exhibited a decreasing trend in the last decade. But the overall

⁎
Corresponding author at: Department of Civil Engineering, Indian Institute of Technology, Delhi, New Delhi, India.
E-mail address: mukeshk@civil.iitd.ac.in (M. Khare).

https://doi.org/10.1016/j.scs.2019.101997
Received 29 July 2019; Received in revised form 29 November 2019; Accepted 29 November 2019
Available online 23 December 2019
2210-6707/ © 2019 Published by Elsevier Ltd.
K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

particulate matter concentration has seen a consistent rise, adding to (Palomino & Martin, 1995). Earlier studies with spatial interpolation
the significance of better inventory creation for it (Nagpure, Gurjar, have observed significantly smaller errors when there are limited to-
Kumar, & Kumar, 2016). A similar study in the Delhi region targeting pographical variations across the study area. It has been seen during the
particulate matter gives us the synergic interaction of various sources assessment of parameters such as ambient temperature with spatial
and what challenges interventions might face (Kumar et al., 2017). interpolation that, in case of mountainous region – the yielded errors
Accuracy did not depend of the nature of site, but adding constraints are large in magnitude when compared to plain or rolling terrain
such as maximum values and daily variation to them can certainly (Chung & Yun, 2004; Kumari, Basistha, Bakimchandra, & Singh, 2016).
provide presentable results. Physical characteristics of site data such as Delhi has a complex terrain in terms of land use but has a fairly flat
geography and concentration variation would be relevant if the factors surface geographically, and hence the probability of predictions with
such as wind speed, temperature dependence of particulate matter and large errors is modest.
topographical variations would be considered. Since the sites were not Although among the two discussed methods, IDW is simpler as
spread over a huge geographical area, these factors would not cause compared to Kriging, yet some studies observed it to outperform the
significant variation in the results. latter (Vorapracha, Phonprasert, Khanaruksombat, & Pijarn, 2015). The
The difference in accuracy is due to the value of the PM2.5 con- satisfactory results obtained in the present study can form the basis of
centrations, and not due to nature of the land use of the sites. In another further evolution by hybrid algorithms such as random forest or neural
work, the health impacts of air pollution have been studied in various networks to improve accuracy and reliability (Qi et al., 2018; Wu et al.,
megacities of India, including Delhi, indicating how hospital visits are 2018). These techniques can also be combined with data from low-cost
correlated with an increase in pollutant concentration (Kumar et al., sensors to improve monitoring networks worldwide (Dünnebeil,
2013). PM2.5 estimations were achieved using two interpolation tech- Marjanović, & Žarko, 2017), and to explore application of Gaussian
niques: Kriging, which is a function of statistical stationarity; and In- framework on Kriging in Delhi region as applied in other Asian loca-
verse distance weightage (IDW) that is a function of the distance of tions (Park, 2016).
separation amongst the sites. In the field of marine pollution, Kriging Even in the latest research works on the prediction of pollutant
regression models are used to create surface maps for biological con- concentrations using geospatial techniques, there are few shortcomings.
tamination and its spreading. Currently spatial interpolation techniques We observe a lack of comprehensive analysis of cross-validation and the
are being used to obtain predicted surfaces for air pollutant con- need to increase the scale to obtain higher resolution predictions. Some
centration also, to obtain reliable high-resolution predictive con- of the relevant works are summarized in Table 1. The specific use of
centration values for major pollutants. these techniques is not done in Delhi, where the geographical distance
Data collection and generation is highly desirable to estimate/pre- between sites was small yet monitoring gaps existed. The use of these
dict the required pollutant (Boznar, Lesjak, & Mlakar, 1993). Moreover, techniques overrules the need for other boundary conditions apart from
high demand for urban air quality estimation models, which help in the geographical coordinates and measured concentrations. In order to
calculating pollutant concentration at a desired discrete location is fill these monitoring gaps, the objective of this work is to obtain reliable
present (Hurley, Physick, & Luhar, 2005). Local geography and the predictions of important, yet unmonitored sites. The quality and the
various meteorological factors such as wind speed, pressure, tempera- interrelation of the considered datasets played an important role in
ture, precipitation in the control volume enclosed by the atmospheric determining the accuracy and the efficiency of predictions. However,
boundary layer, have a contrasting effect on pollutant estimation considering the scope of the study and future applicability, the results
(Baklanov, Korsholm, Mahura, Petersen, & Gross, 2008). Nevertheless, are encouraging. IDW and kriging used in this study can target three
it is not possible to consider the synergic effect of all such factors during major challenges: (i) proxy PM2.5 developments in case of insufficient
physical modelling. Hence, pollutant data across India from Nation- ambient air quality measurements station; (ii) imputation of incon-
wide Ambient Air Quality Monitoring Network (NAAQM) program is sistent information on daily PM2.5 concentrations; and (iii) identifica-
relied upon. Moreover, the dispersion of these pollutants, rather ran- tion of high and low PM2.5 hotspots and episodes.
domly in the lower layer of the atmosphere also introduces a varying
degree of uncertainty (Mallet & Sportisse, 2008). The spatial and tem- 2. Study area
poral distribution of the pollutants can be estimated using multiple
basic laws of physical sciences such as equations of mass, energy, mo- Delhi, the capital of India, is a second most populated city of India,
mentum conservation; but in addition to gas laws and thermodynamic narrowly surpassing Mumbai (World population review, 2019) in the
parameters, one requires multiple boundary conditions at each grid north of the country. New Delhi is one of the urban districts of Delhi
boundary. In recent studies, kriging based regression model has been and the seat of all three branches of Government. There has been rapid
used to quantify the radioactive soil contamination. urbanization and a corresponding increase in traffic and energy con-
Kriging based techniques have been used in structural analyses, sumption. Moreover, there has been growing evidence that ambient
specifically to analyse Timoshenko beams where conventional poly- PM2.5 levels of are observed to be highest in Delhi (Gupta et al., 2007;
nomial interpolation was usually used (Wong, Sulistio, & Syamsoeyadi, Shukla, Ojha, & Khare, 2018), and the concentrations have even tou-
2018). Monte Carlo Techniques combined with Kriging have used for ched 999 μg/m3 in the worst months (Mukherjee et al., 2018). The
Reliability Analysis of Mechanical System Models. It has helped to vehicle count has exhibited a surge in the last decade which leads to an
overcome specific drawbacks of using small failure probabilities increased vehicular density. This contributes to higher pollutant con-
(Lelièvre, Beaurepaire, Mattrand, & Gayton, 2018). In a recent study in centrations apart from other problems (Panwar, Agarwal, & Devadas,
Central Italy, Kriging based regression model was used to quantify the 2018). Considering the significance this city holds in terms of the
geogenic radon potential and subsequent exposure risk from the con- economic, cultural and industrial growth along with being the inter-
taminated soil (Giustini, Ciotoli, Rinaldini, Ruggiero, & Voltaggio, national gateway to the world, it is crucial to ascertain the sustain-
2019).Ordinary Kriging, Regression Kriging and Co-Kriging were used ability of the city in terms of infrastructure and the massive population
to map potentially toxic metal concentrations in Southern China (Xu it resides.
et al., 2019). In another recent study, Kriging regression models were The temperature of the city rises to as high as 45 °C, in the summer
used in estimating the surface contamination of biological origin (Rossi months of April to June, whereas it falls to the lowest of 8 °C in the
et al., 2018) winter months of December to January. The annual average tempera-
Metrological parameters such as wind speed are profoundly affected ture is 25 ± 7 °C for the study duration of 2015–2017. The monitoring
by the terrain of a site and these methods have also been previously stations and target locations (where predictions for PM2.5 are made) are
modelled in various studies using unadorned methods such as IDW shown in Fig. 1. Location coordinates are superimposed on a shape-file

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K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

of Delhi in ArcGIS (version 10.2).

Rosenlund et al. (2008)

De Hoogh et al. (2008)
Dalmau et al. (2017)
Majority of the monitoring stations are maintained by the Central

Mercer et al. (2011)

Zaytar et al. (2017)

Hoek et al. (2008)

Shad et al. (2009)
Pollution Control Board (CPCB), Delhi Pollution Control Committee

Lin et al. (2018)

Xu et al. (2019)
(DPCC) and the Indian Institute of Tropical Metrology (IITM), Pune.
Reference

Monitoring data is accessible to both public/institutional bodies and

individuals. However, there is a lack of a comprehensive network of
monitoring stations, which are sometimes not practical to maintain.

2.1. Site selection and characteristics

Ordinary Kriging is a kind of Universal Kriging
Critical areas in the north of the study area.

Emission data did not bring variation in R2

First high-resolution LUR models produced

Among 36 monitoring stations located within Delhi, only 17 mon-

Statistical interpolation is most practical
Kriging potent as a prediction technique

itored PM2.5 concentrations for the study period of January 2015 to

Kriging improves the quality of LUR

December 2016 and November 2017 to February 2018. This highlights

the need to use modelling-based prediction techniques to get depend-
able concentration estimates for these and other sites. Traffic and in-
dustrial hotspots, dense residential areas and other areas of maximum
Kriging proved reliable
IASI instruments used

exposure were considered in ascertaining the target locations (Yedla &

Shrestha, 2003). The residential zones listed face the huge magnitude of
traffic flow daily. Hence PM2.5 becomes a significant cause of concern
(Pandey, Kumar, & Devotta, 2005). Institutional areas, which are away
Remarks

from the industrial areas, though devoid of most pollutants, still have
large exposure to PM2.5 (Brunekreef & Forsberg, 2005). These sites are
listed in Table 2, along with the characteristics.
The sites under study lie in Delhi, which is a major hotspot of in-
Hybrid class of models appeared most suited
GAs reduce the estimated error significantly

dustrial and economic significance for the country and holds a promi-
Land-use regression give well-fitting curves

nent place globally as well (Desai & Vanneman, 2018). Although, the
methods are simple, they provide a reliable estimate of PM2.5 con-
centrations at few target sites of significant importance, where instru-
Models significant in predictions
Fitting error of Bilonick smallest

Kriging steadily outperformed

mental monitoring is not feasible due to logistic or financial constraints.

Data processing system used

The city under study is host to a large population which is residing in

Universal Kriging best

relatively smaller area, contributing to high population density. Air

Improved robustness

pollution, especially particulate matter is threatening the sustainability

of the city and posing a potential hazard to the significant population
Major findings

size. Working in synergy with other contributors, robust input about the
estimate of this perilous pollutant, can ascertain the sustainability of
the city and adjoining satellite towns (Bikkina et al., 2019).
Delhi exhibits a mixed land use pattern, making the traffic density
higher and increasing the exposure to synergic air pollutants (Kumar
et al., 2015). PM2.5 has a high potential to affect the people living in
Regression-based improvement

100 m x 100 m Hybrid models

Comparison: STK and Kriging

areas shared by various other types of land use (Mohan, Pathan,

LUR and Kriging evaluated
Genetic algorithms (GAs)

Narendrareddy, Kandya, & Pandey, 2011)

Review of past studies on spatiotemporal analysis-based air pollutant prediction.

Prediction using HPC

The scope of the study is not expanded to monitoring sites of NCR,

Land-use regression
AMDAR improved

due to possible error formation from long-range extrapolation. The

Models reviewed

distance between monitoring sites of Delhi and locations of NCR is very

Study focus

high as compared to the inter-site distance inside Delhi itself. The

identified monitoring stations undertake 24 -h monitoring in 3 batches
of 8 -hs samples for PM2.5. Due care is taken to ensure that the standard
guidelines are followed while monitoring and data inventory as CPCB is
the authority to ascertain the guidelines. Additionally, the data were
Target pollutant/ parameters

screened for any discrepancies of negative or zero concentrations along

with certain unexplained spikes in the concentration, attributing them
(CH4), (CO2) and (N2O)
PM2.5, NO2, O3 and BC
Wind and temperature

to monitoring errors.
PM2.5 concentrations are adopted from above-mentioned mon-
itoring stations for two-phase durations: 24 months’ data from 4 sites,
and 4 months’ data from 17 sites. Some data discrepancies have been
and NO2

observed, as noted in Table 2. The highest PM2.5 concentrations among

PM2.5

PM2.5

PM10
NO2
NO2
NOx

adopted 24-month data are documented at Anand Vihar monitoring

station in January 2016 (i.e. 329 μg/m3), whereas the lowest value
(28 μg/m3) is recorded at Mandir Marg for the month of July 2016. The
Los Angeles, CA, USA.

time series of PM2.5 datasets from January 2015 till December 2016 is
presented in Fig. 2. Furthermore, Fig. 3 shows the recorded levels of
Hamilton, Canada
Western Europe

PM2.5 from November 2017 till February 2018 under three site cate-
Beijing, China

Tehran, Iran
Rome, Italy

gories.
Morocco
Location

For the 4 months’ data, the peak is observed at Anand Vihar, during
Table 1

China

Spain

the month of November 2017 (i.e. 330 μg/m3). On the other hand, the
lowest value is exhibited by Lodhi Road at 90 μg/m3 for the month of

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K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

Fig. 1. Monitoring stations and target locations. The distance between two prominent sites (Punjabi Bagh and RK Puram) is marked for a scale reference.

Table 2
Characteristics of monitoring stations and target locations.
Characteristic

Site Name Location (Longitude, Latitude) Monitoring site/ Target Location Land Use/ Major Activity

Anand Vihar a 28.650278N, 77.302778E Monitoring Site Transport

RK Purama 28.56611N1, 77.176667E Monitoring Site Residential
Punjabi Bagha 28.661944N, 77.124167E Monitoring Site Residential
Mandir Marga,d 28.634167N, 77.200556E Monitoring Site Commercial
Aya Nagar 28.468881N, 77.127188E Monitoring Site Residential
Burari Crossing 28.728343N, 77.197495E Monitoring Site Residential
CRRI Mathura Road 28.551003N, 77.273836E Monitoring Site Institutional
DTU 28.749981N, 77.117236E Monitoring Site Institutional
IGI T3 28.554927N, 77.0844E Monitoring Site Transport
IHBAS, Dilshad Garden 28.68115N, 77.304583E Monitoring Site Institutional
ITO 28.627521N, 77.243774E Monitoring Site Commercial
Lodhi Road 28.59246N, 77.236729E Monitoring Site Commercial
NSIT, Dwarka 28.609088N, 77.03465E Monitoring Site Institutional
North Campus b 28.687613N, 77.21023E Monitoring Site Institutional
PUSA 28.63432N, 77.170913E Monitoring Site Institutional
Shadi Pur 28.652533N, 77.155121E Monitoring Site Commercial
Siri Fort 28.54991N, 77.219907E Monitoring Site Residential
Mukarba Chowk 28.734917N, 77.15579E Target Location Industrial
ISBT Kashmere Gate 28.669133N, 77.232001E Target Location Transport
Peeragarhi 28.67974N, 77.092688E Target Location Transport
AIIMS 28.567116N, 77.210046E Target Location Industrial
Geeta Colony 28.653868N, 77.271231E Target Location Residential
Shahdara 28.698056N, 77.290423E Target Location Residential
Shalimar Bagh 28.716447N, 77.154089E Target Location Residential
Connaught Placec 28.63281N, 77.219421E Target Location Commercial
IIT Delhic 28.545042N, 77.192465E Target Location Institutional
Tilak Nagar 28.63858N, 77.084849E Target Location Residential
Rithala 28.718362N, 77.105188E Target Location Residential

a
Additional 4 months data apart from 24 months data is taken for these sites.
b
No data available for November 2017 from this monitoring site.
c
No Kriging-based predictions are obtained for these sites for June 2015; July 2015; December 2015 and February 2016 to June 2016.
d
No data available for August 2016 for this site.

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K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

Fig. 2. 24-Month time series of PM2.5 concentrations from 4 monitoring stations.

February 2018. which is a stochastic method; and Inverse Distance Weighting (IDW),
which is a deterministic interpolation method. Apart from the statistical
2.2. Interpolation and cross-validation and deterministic techniques, LUR and dispersion modelling are also
used extensively to make air pollution predictions. Both of the model-
A better database of pollutant data can be compiled if a spatial point ling techniques have already been researched on both local and re-
estimation process is developed, although, there exists no best method gional scales. Another interpolation technique available in ArcGIS is a
to interpolate any data set. Some criteria to choose among the available spline function. It was not used for the study as it is better for datasets
methods could be the accuracy level required, characteristics of the which exhibit mild variability, but we observe high seasonal variability
data available and the computer/human resources at disposal (Lin, Mo, in PM2.5 concentrations. Since different techniques yield different var-
Li, & Li, 2002). iations for the same data set, multiple methods need to be studied with
Current work applies two spatial interpolation techniques: Kriging, regarding their surface analysis. Kriging is a geostatistical process,

Fig. 3. 4 Months monitored data for (a) Residential, (b) Transport and Commercial and (c) Institutional Land Use Monitoring sites.

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K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

which defines a correlation (semivariogram) among the sample points; 2.5. Statistical stationarity and the nugget effect
it is used to model the spatial variation in the pollutant concentration.
Application of the methods for Delhi PM2.5 concentrations have been Statistical Stationarity considers the total set of observed data points
carried out due to two reasons. Firstly, it is a variable which is spatially as a single variable series. Additionally, a system of repetition must be
distributed and secondly, it appears to be correlated across well-defined realized to develop any kind of deduction procedures; and if not pre-
geographical regions (Jerrett et al., 2005). Base data for geospatial sent, created. Nugget effect refers to the discontinuity towards the
analysis is the monthly average data, obtained from 24 -h daily origin of the semivariogram. This discontinuity is reported to be caused
averages for PM2.5 from NAAQMs stations in Delhi. These stations by measurement errors and micro-variability in the spatial phenom-
provide hourly, 8 hourly and 24 hourly averages of various air pollu- enon being considered (Howarth, 1978). In the current study, due to
tants along with values of temperatures and other meteorological the ‘absence’ of statistical stationarity in the data set, ‘pure nugget ef-
parameters. The 24 -h average of PM2.5 at the stations were obtained fect’ was observed. Kriging failed in predicting the required values for
from the stations and converted to monthly averages after filtering out June, July and December of 2015, and February to June of 2016. One
zero and negative values attributed to measurement and instrumenta- month’s variogram, where Kriging failed because of pure nugget effect,
tion error. is shown in Fig. 4(b).
We used a tool “geostatistical analyst” in ArcGIS to analyse spatially
varying data inventory and generation of the two-dimensional surface 2.6. Cross-validation of concentration measured at monitoring sites
using measured data while employing advanced statistical techniques.
Spatial interpolation provides us with the best representation for a For cross-validation, recorded PM2.5 concentrations from 3 mon-
surface and helps in predicting the required values of unmonitored itoring stations are used to predict the value at the 4th site. This is then
sampling points to create a comprehendible surface (Johnston, Ver compared with the measured value at the 4th site, to obtain a percen-
Hoef, Krivoruchko, & Lucas, 2001). Spatio-temporal analysis of the tage error. These errors give an estimate as to how well has the semi-
pollutant helps to make informed policy changes and to concentrate variogram been fitted over the plotted data points, and how dependable
mitigation efforts at critical locations which can be identified (Boiné, the predictions will be. Fig. 5(a) and (b) represent the error between
Demers, & Potvin, 2018) measured and predicted values at 4 monitoring sites (for 24-month
PM2.5 data) and 17 monitoring sites (for 4-month PM2.5 data), respec-
tively.
2.3. Inverse distance weighting
PM2.5 concentrations have been mapped and estimated using
Kriging and IDW techniques in multiple studies (Xie et al., 2017) and
IDW interpolation explicitly works on the assumption that things
they are authentic prediction techniques as per credible references (Wu
which are closer to each other are more alike than those which are
et al., 2018). Whereas, superior modelling development requires ex-
farther apart. Greater weight will be assigned to the points which are
tensive work on the development which would reduce the scale of the
closest to the target location, and hence the allocated weights change as
current study and divert the purpose of the study towards a develop-
an inverse function of ‘pth power of distance’, where power function (p)
ment-centric modelling criteria (de Hoogh et al., 2018). The major goal
is a positive real number. Greater values of p grant greater influence on
of the study had been to provide a comprehensive, ready-to-use mapped
values which are closest to the point to be interpolated. The parameter
and predictive estimate of PM2.5 blanket over the city. Inclusion of
prediction for the target location is a summation of the product of ‘al-
various metrological factors along with 3D building information and
lotted weights’ and ‘measured values’ for all sites. After reviewing nu-
land use analysis would further require feasibility studies, which can be
merous literature, p is taken to be 2 for the current study.
an interesting study area for research in future, although, for the im-
mediate requirement of PM2.5 estimates at indispensable sites of Delhi,
2.4. Kriging – ordinary this holds less relevance as the land use and topography is homo-
geneous (Ahmad, Ahsan, & Said, 2019).
Kriging offers some advantages over other interpolation techniques.
It interpolates using weights independent of the data, hence practically, 3. Results and discussions
the weighs after the first estimation can be used for all data sets. Also, it
is an ‘exact’ interpolator i.e., estimate at any observational point is the 3.1. Predictions based on 2-year data
observation itself (Zimmerman & Homer, 1991).
Kriging has a smoothening effect on the result where it over- Predictions were made at two locations: IIT Delhi campus and
estimates the higher values and underestimates the lower values. Since Central Park, Connaught Place using PM2.5 concentration data for each
the data has a smooth trend with lesser daily fluctuations, this was not a month from the period January 2015 to December 2016 from 4 mon-
cause of concern in the study. itoring stations (Anand Vihar, Punjabi Bagh, Mandir Marg and R K
The necessary steps to predict with Kriging are uncovering the rule Puram). Both IDW and Kriging predictions were archived for the two
for getting the dependence and making estimations. The most sig- locations, and the predicted concentrations are plotted against each
nificant contribution of Kriging based dependence estimation is the other as shown in Fig. 6.
effect of ‘statistical stationarity’ in few cases of predicting values. Some The predictions at IIT Delhi showed a peak (274 μg/m3) in
data sets are observed to be random to the extent of contributing to a November 2016 using the IDW technique. On the other hand, the
situation, in which the prediction methodology fails to establish any lowest value (41 μg/m3) is exhibited during August 2016 at using the
correlation to carry out dependable estimation. This is termed as a same technique. Moreover, the peak prediction for Connaught Place is
condition of ‘pure nugget effect’ which was observed in the months of noted to be 271 μg/m3 during November 2016 using Kriging, while the
June, July and December of 2015, and February to June of 2016. One lowest value (31 μg/m3) is exhibited for July 2016 at Connaught Place
month’s variogram, where estimation failed because of pure nugget using the IDW technique.
effect, is shown in Fig. 4(b).
Other prediction techniques fail to identify this situation and lead to 3.2. Predictions based on 4 months’ data
highly inaccurate estimations. Variograms and covariance functions are
created to predict the required relationship called the statistical de- Fig. 7 shows the predictions using four-month PM2.5 data from
pendence (and called spatial autocorrelation). A sample variogram for multiple monitoring stations. The IDW technique on the 4-months data
the month of December 2017 is shown in Fig. 4(a). for Residential and Institutional prediction locations showed the peak

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K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

Fig. 4. (a) Semivariogram exhibiting curve fit through covariance between concentration values of PM2.5 for December 2017. (b). Pure Nugget Effect observed for
June 2015 exhibiting failure of Kriging method.

(305 μg/m3) in November 2017 (i.e. at Rithala) as opposed to lowest effective in predicting the values for these months. IDW is more effi-
values (114 μg/m3) for the month of February 2018 at Shahdara. When cient in identifying pollution hotspots from the mapped prediction
it was used for Industrial, Transport and Commercial prediction loca- surfaces. Kriging tends to have a ‘smoothening’ effect. But Kriging is
tions, the peak (216 μg/m3) is again observed in November 2017 (i.e. at more effective in predictions when the number of input points are
Peeragarhi) while the lowest value (116 μg/m3) is exhibited in February higher and spatial orientation is important. This is noted in phase II of
2018 at ISBT Kashmere Gate. the study when PM2.5 data from 17 monitoring stations were used.
When the Kriging technique was used for PM2.5 prediction using the Similar effects have been observed in a study of Arsenic contaminated
4 months’ data for Residential and Institutional prediction locations, soil samples (Qiao et al., 2018). For applications related to health im-
the peak (267 μg/m3) is observed in November 2017 i.e. at Rithala. On pact assessments, the use of hybrid methods that combine air quality
the other hand, the lowest value (116 μg/m3) is exhibited for the month model outputs with observational data is suggested to obtain effective
of February 2018 at Shahdara. When it was used for Industrial, results. A large-scale study has been conducted in the Atlanta region of
Transport and Commercial prediction locations, the peak (263 μg/m3 at Georgia which compares various techniques and explore the said hybrid
Peeragarhi) are again observed in November 2017 while the lowest models (Yu et al., 2018). In a case when multiple pollutants are se-
value (122 μg/m3) is exhibited for the month of January 2018 at, at lected, for instance, PM10 and PM2.5, Kriging seems to perform better
AIIMS. The process of cross-validation is available in the geostatistical with PM10 and IDW is more suitable for PM2.5. A recent study (Lin,
analyst of ArcGIS. The effectiveness of the fitted semivariogram is the Zhang, Chen, & Lin, 2018) conducted in Shanghai, China, reported si-
measure of how accurate the predictions would be. The plotted per- milar results. Other studies have established that increasing the geo-
centage errors in Fig. 5a, b show how well the semivariogram had fit. It graphical area under consideration causes the predicted values to be
also gives an estimate of how dependable the predicted values using unreliable as the distance between monitored sites and target sites in-
these semivariogram would be. creases, leading to uncertainties. The uncertainties are pertaining to
inaccuracies in predictions as percentage error in cross-validation in-
crease significantly. Considering one of the recent studies (Xu et al.,
3.3. Predicted surfaces 2019), the error analysis of predicted results indicates that as the dis-
tance increases, reliability reduces. Recently, Qiao et al. (2018) com-
Fig. 8a shows the predicted surfaces for the first phase i.e. No- pared Ordinary kriging with IDW while studying soil pollution in China
vember 2017 to February 2018 and in Fig. 8(b) and (c) for January and identified better prediction accuracy for IDW. Like this study, other
2015 to December 2016. The trend observed in the predicted value is techniques (Kriging based) were used where Ordinary Kriging failed to
like the trend observed in the monitored values, apart from the varia- predict maximum and minimum concentrations.
tion in magnitude. As per the extensive study of the past researches on PM2.5 using
Kriging exhibits failure for the months of June, July and December Kriging and IDW, the variation in error percentage is subject to the
for 2015 and February to June for the year of 2016. IDW proves to be

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K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

Fig. 5. (a) Percentage error between the measured and predicted value at 4 monitoring sites for 24-month PM2.5 data (b) Percentage error between measured and
predicted value at 17 monitoring sites for 4-month PM2.5 data.

geographical location of the site and their relative position with respect effect of wind speed on the predicted values has been studied in the
to each other and with the target location at which the value needs to Kocaeli region of Turkey (Erener, Sarp, & Yıldırım, 2019). Adding the
be estimated. Larger grid sizes and therefore larger effective distances effect of wind speed to future studies would give better results. PM2.5
between sites of concern leads to higher errors in predictions (Alexeeff also affects the indoor air quality in places which are densely populated
et al., 2015). Higher resolution studies cause the effective distance and residential zones are located closer to traffic and highways (Martins
between sites and the variation in concentrations to reduce leading to & da Graça, 2018). Modelling techniques have been used to predict the
more accurate predictions (Hu et al., 2019) effect of outdoor air quality on the indoor air quality highlighting the
Another recent study in Madrid, Spain (Gómez-Losada, Santos, effect (Karri et al., 2018).
Gibert, & Pires, 2019) observed the effect of Urban Heat Island on the Prediction of pollutant concentration using Kriging and IDW tech-
predicted pollutant values. Delhi is also known to be affected by the niques has acceptable dependability and the future scope of combining
same phenomenon and hence the higher percentage errors in predic- it with other spatial interpolation techniques is vast. If metrological and
tions for the summer months can be attributed to this. Additionally, the physical influences can be combined with the raw prediction results

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K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

Fig. 6. Predicted PM2.5 Concentrations at IIT Delhi and Connaught Place using (a) IDW and (b) Kriging.

from Kriging and IDW, the reliability of the predictions shall increase programming. Further work towards ascertaining the statistical statio-
manifold. These techniques can be applied without the boundary con- narity of the data without going through the Kriging process could
ditions of having a grid which makes them versatile and usable for cases provide an added advantage. This would lead to realising that the
where the monitoring sites are scattered. method has failed for the data set at hand at the semivariogram stage
Improved interpolation techniques beyond simple Kriging and IDW only. In turn, if the datasets were to be segregated while using other
have been developed as Probability Kriging, Disjunctive Kriging and prediction techniques such as IDW (if required), both man hours and
Empirical Bayesian Kriging which are used for other applications, apart computational power can be reduced.
from air pollution prediction. Moreover, hybrid techniques have been PM2.5 mapping methods used in this study can act as a baseline for
developed which incorporates spatial interpolation technique (Kriging) various hotspots within the city, which are growing at an appreciable
and regression analysis that can produce a detailed prediction map with rate in terms of the population of people and road vehicles as well as the
improved accuracy and prediction dependability (Yao et al., 2013). Yet, need for the total energy (Gulia, Nagendra, & Khare, 2017; Kumar et al.,
combining the two spatial interpolation techniques would require re- 2013; Shukla et al., 2018) The mapped pollutant profile of concentra-
programming of the techniques, validation of which can be studied tions can ensure that the policy changes and future town planning
through future studies. Therefore, apart from their aid to interpret re- provisions are in accordance with the goal of mitigating the pollutant
sults, combining them into a hybrid technique is beyond the scope of concentrations (Chowdhury et al., 2019).
the current study, but can certainly make an interesting area of interest
for future research.
There is a possibility of reducing the temporal scale of the study to 4. Summary and conclusions
daily and even hourly concentrations by integrated advanced computer
PM2.5 is the major contributors to the health, transport and

Fig. 7. Predictions for (a) residential and institutional locations (Kriging), (b) for Industrial, Transport and Commercial locations (IDW), (c) residential and in-
stitutional locations (Kriging) and (d) residential and institutional locations (IDW), between November 2017 and February 2018.

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K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

Fig. 8. (a; upper panel): Predicted surfaces using (i) IDW and (ii) Kriging for November 2017 to February 2018; (b; middle panel) IDW Predicted surfaces January
2015 to December 2016 at IIT Delhi campus and Connaught Place; (c; lower panel): Kriging Predicted surfaces January 2015 to December 2016 at IIT Delhi campus
and Connaught Place.

infrastructural challenges faced by the city. The study has utilised included in the study by using 4-month data (November 2017 to
monitored concentrations of PM2.5 at various monitoring stations across February 2018). PM2.5 concentrations predictions yielded an average
the city of Delhi to predict corresponding values at other sites of interest error percentage of 23 % by both IDW and Kriging individually. Thus, it
in the city. We used two methods of interpolation: a deterministic is challenging to conclude one of the two methods better, although, for
technique namely Inverse Distance Weighting and a statistical method the gaps, where Kriging fails to interpolate due to the absence of data
namely Kriging. Cross-validation analysis concluded that 24-month stationarity, IDW fills in well.
PM2.5 concentrations exhibit errors of the magnitude as 19 % and 17 % Within the scope of this work, there was no procedure to ascertain
for 2015, and 27 % and 26 % for 2016, for IDW and Kriging, respec- the verification of statistical stationarity, hence some of the results from
tively. Additionally, in phase II, when 17 monitoring stations were the Kriging technique are omitted. The prediction, in this case, results

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K. Shukla, et al. Sustainable Cities and Society 54 (2020) 101997

in constant value over the whole of the predicted surface. Kriging is analysis of air pollution parameters to meteorological data (Kocaeli/Turkey). Advances in
unable to interpolate data that is not statistically stationary. To ascer- remote sensing and geo informatics applications. Cham: Springer355–358.
Fotourehchi, Z. (2016). Health effects of air pollution: An empirical analysis for devel-
tain the statistical stationarity of the data beforehand is a tedious oping countries. Atmospheric Pollution Research, 7(1), 201–206.
process which is itself an emerging research topic and requires ex- Giustini, F., Ciotoli, G., Rinaldini, A., Ruggiero, L., & Voltaggio, M. (2019). Mapping the
tensive use of high-level computing tools. The formulated PM2.5 the- geogenic radon potential and radon risk by using Empirical Bayesian Kriging re-
gression: A case study from a volcanic area of central Italy. The Science of the Total
matic maps can eventually provide a basis for efficient actions to con- Environment, 661, 449–464.
trol air pollution and further handle various societal and technological Gómez-Losada, Á., Santos, F. M., Gibert, K., & Pires, J. C. (2019). A data science approach
challenges. for spatiotemporal modelling of low and resident air pollution in Madrid (Spain):
Implications for epidemiological studies. Computers, Environment and Urban Systems,
75, 1–11.
Funding and acknowledgements Greenstone, M., & Hanna, R. (2014). Environmental regulations, air and water pollution,
and infant mortality in India. The American Economic Review, 104(10), 3038–3072.
Gulia, S., Nagendra, S. S., & Khare, M. (2017). A system based approach to develop hybrid
This work has been supported by the University grant commission –
model predicting extreme urban NOx and PM2. 5 concentrations. Transportation
Junior Research Fellowship, India, and also the Natural Environmental Research Part D: Transport and Environment, 56, 141–154.
Research Council [grant number NE/P016510/1] through the project – Gupta, P. K., Singh, K., Dixit, C. K., Singh, N., Sharma, C., Sahai, S., ... Garg, S. C. (2007).
An Integrated Study of Air Pollutant Sources in the Delhi National Spatial distribution in aerosol mass and size characteristics between Delhi and Hyderabad
during land campaign in February 2004.
Capital Region (ASAP-Delhi) – under the UK-India NERC-MOES Heal, M. R., Kumar, P., & Harrison, R. M. (2012). Particles, air quality, policy and health.
Programme on Air Quality and Health in Megacity Delhi. Chemical Society Reviews, 41, 6606–6630.
Hoek, G., Beelen, R., De Hoogh, K., Vienneau, D., Gulliver, J., Fischer, P., & Briggs, D.
(2008). A review of land-use regression models to assess spatial variation of outdoor
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The authors have no known competing financial interests or per- Geostatistics in the Mining Industry. Dordrecht, Holland (D. Reidel Publishing Co.),
1976. xvi 461 pp., 126 figs. Price Dfl. 105.OO ($39.50). Mineralogical Magazine,
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reported in this paper. Hu, H., Hu, Z., Zhong, K., Xu, J., Zhang, F., Zhao, Y., ... Wu, P. (2019). Satellite-based
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